Implementation of a new variant of chess

ABSTRACT

Implementation of a new variant of chess characterized because it has the following elements: a central processing unit for storing a database of reference, a database of reference created from all recorded chess games in history divided by categories, a selection and filtering process based on a specific algorithm that selects one single game in order to stablish the initial position of the new game, a chess software for installation in any device, electronic devices to play the new game online and unlimited number of users to play the game live; and because the starting position of the game is determined at random just before the start of play, being unknown by the players until the beginning of play and wherein the procedure for obtaining that initial position consists of setting a certain specified number of full moves, said number being called depth, from the starting position of classical chess and being the depths numbers all up to 10 and either integers, except 0, or the result of adding an integer plus 0.5; selecting at random one game from a single reference database made of high-skill human classical chess play and regularly updated; and initiating the game from the initial position the player with the white pieces if the depth number is an integer, otherwise the black pieces would initiate the game.

BACKGROUND OF THE INVENTION

The present invention relates to chess games and, more specifically, toa new chess variant and method of play thereof affecting the beginningof the game, along with its implementation.

DESCRIPTION OF PRIOR ART

Classical chess (or simply “chess”) is a game of skill for two players,played upon an eight-by-eight square, checkered board. Chess rules andmovements of the pieces have been essentially unchanged for severalhundred years, except some minor unifications more than a century agowhich have resulted in a game which is played across the globe in thesame manner.

Chess from its origins has been an “almost infinite” game, where thecombinatorial explosion of possibilities gives raise to so manydifferent positions that playing skill and talent have been moreimportant, and overwhelmed attempts at memorising most possible coursesof the game.

There have been proposals to modify classical chess, or alter its rules.The reason behind this is that widespread and intense study of the gamehas made many strategies and aspects of it deeply analyzed, compromisingcreativity and, crucially, “over-the-board” discovery of the moves onthe part of the players. Most importantly, in the last 15-20 years, thegrowth of opening theory together with generalised access tocomputer-aided preparation have enabled rote memorization of openinglines (i.e. initial sequences of moves by both players) to have a strongimpact on elite competitions, as well as on competitive professional andamateur events (see the work by Kasparov in the References).

Chess variants proposed in the past have often entailed the creation ofnew pieces for use along with classical chess pieces, as well as newboards or rules. However while on an abstract level these variations mayoccasionally be as interesting (or more interesting for some) as theclassical game, and have achieved some popularity, they have not made amajor impact on the chess-playing world. The reason, we believe, is thatthe history and tradition of the game is so strong and has created sucha paramount shared heritage, that most chess lovers find any substantialchange to the way the game is played (change of any of: board, pieces orrules) as “alien” and devoid of any attraction. We will thus not followthis first line of invention in the present work. We have concluded thatchanges to the game of chess that feature such profound alterationsresult simply in wholly different games, and do not offer any hope ofcreating a variant of the game satisfactory for the current classicalchess community.

There has been another, very different, second line of invention,Fischer-Random (“FR”) chess, (advocated by former American chess WorldChampion Robert J. Fischer) now-called chess960, which in the pursuit ofa variant of the game has avoided changing the board or adding newpieces, or any rule of the game except the initial position of thepieces. This initial position is obtained from a random reshuffling ofpieces before the start of the game, within each of two rows wherepieces lie in the initial classical chess position (i.e. the first andlast ones, or the two that are closest to each player, where all thepieces but the pawns lie). From then onwards, the game proceeds as inclassical chess. The resulting game is much closer to the original gameof chess than the variants discussed above, and has gained acceptanceand some popularity. FR chess has also been accepted as a relevant, ifstill a minority part of the chess world (see References herein aboutthe Fide Handbook) while it has not challenged in practice the dominanceof the original form of the game.

We believe it is logical and deserving that FR has achieved a higherstanding in the chess world than variants from the aforementioned, firstline of invention. FR chess is not an “alien” game to chess players.However, still the weight of chess tradition and the profound influenceof the initial position of the pieces in the development of the openingand middle-game phase of the game, have made widespread popularity of FRchess elusive. It is noteworthy to what extent the importance oftradition for the chess community has been yet again confirmed. Notethat as the initial classical chess position is one in 960 positions,the history of the classical game is roughly 0.1% of the possibledevelopment of FR going forward, hence history is not fully obliteratedbut almost so—it has an extremely minor role in FR chess, as has beenindeed the intent of its advocates. Another chess variant along the sameline of invention than FR is Random Opening Chess, also interesting butwhich has not gained any of the popularity of FR chess, and has the sameissues as FR chess but to a greater extent, so we will only mention ithere.

We consider the present invention to be in the same line of invention asFischer-Random chess, as only the starting position of the game ismodified, but not any other rule or its board and pieces, while suchstarting position is determined at random just before the start of play.

We conclude the description of prior art with the observation that nochess variant that has ever been invented up to now seems to be closeenough to classical chess for the tastes of the current chess globalcommunity, i.e. providing the empirical lesson that no modification ofchess that does away with its legacy and tradition is good enough, inthis sense, as an alternative for such community.

Purpose of the Invention

To provide a new variant of chess and its implementation, that is assimilar to classical chess as possible and preserves its legacy andtradition, while it substantially diminishes the role of rotememorization of the opening phase, which has recently been steadilyincreasing due to the impact of computer-aided preparation. Specifically

-   -   1. There is no change to the board, the pieces, or the rules.    -   2. Only the initial position may differ from classical chess,        and is uncertain, i.e. not known until just before the beginning        of play, and taken at random from a known collection of        positions which is representative of actual contemporary master        (i.e. skilled) competitive play.    -   3. It fully integrates and preserves the legacy of chess within        the realms of the new game.    -   See 2.4 below for a more accurate description.

We rephrase the purpose of the invention in the following aspirationalway:

To provide an “evolution” of classical chess, i.e. not a mere variantbut a method of play that introduces uncertainty in the initial positionwhile the legacy of chess is preserved, hence along with it the revealedpreferences of the current classical chess community. We intend such anevolution to have, for the first time in the history of chess variants,the foundation to aspire to become a widespread alternative orcomplement to classical chess.

The author has denominated his invention “Neoclassical chess”.

Specific Problem Solved by the Invention

The objetive of the present invention is to develop a new variant of thegame of chess that solves the issue of the excessive memorization of theopening phase while preserving the rules, tradition and legacy of theclassical game of chess, along with its implementation. We have definedin what follows the requirements that such a new game (which we call“neoclassical chess”) should satisfy:

(i) It is a game equal to chess, except in its initial position, and theplaying set-up process is simple as in chess.

(ii) It starts from a balanced initial position i.e. as balanced as thatof classical chess and includes and preserves its legacy. All masterchess games are possible “neoclassical chess” games (except for rareexceptions: if they feature an incorrect opening or are not relevantfrom a competitive viewpoint), a property which we denominate “backwardcompatibility” with classical chess. Reciprocally, all future“neoclassical chess” games are possible as games of classical chess¹,which we call “forward compatibility” with classical chess. ¹ i.e.considering its development as appended to the concrete, initialsequence of moves leading from the initial position of classical chessto the initial position of neoclassical chess, as it will be clarifiedlater.

(iii) It must reflect the opening preferences of contemporary skilledhuman play, with the capacity to evolve and incorporate futurepreferences through a systematic, non-arbitrary process.

Additionally, we have aimed to modify classical chess in the leastpossible degree, the strict minimum needed to solve the problem, and toaccomplish this in a reproducible, non-arbitrary manner.

Mathematical Framework

In order to develop the new game, we have built a logical framework thatdelineates our objective from a mathematical perspective. The problemhas been reformulated as a “constrained optimization” problem within theset of all variants of chess which fulfill the three requisitesmentioned above. The objective is to find the one among these which isclosest to chess and verifies a certain constraint: there must besufficient uncertainty about the initial position of the chess variantso that the value of opening preparation based on rote memorisation isin practice greatly diminished, as it is very difficult to accomplishand unlikely to be useful (because of the large number of possible linesand the high likelihood of forgetting such preparation in time). Theconstraints are expressed as restrictions on the cumulative distributionfunction of chess positions (taking into account transpositions) atseveral key probability levels of the validity of the preparation.Please see Appendix I for an illustration of the mathematicalformulation of such constraints.

BRIEF SUMMARY OF THE INVENTION Novelty and Uniqueness of the Invention

The invention we propose is the only known chess variant that achievesrandomness by choosing its initial position in the following manner: agame is chosen at random from a database of relevant contemporary masterchess games, and the position after an initially specified number ofmoves is selected, to be used as initial position in the new inventedgame.

Hence it uses a single reference database of games that represents thestate of the art in relevant games between players of sufficiently highskill, so that a randomly chosen, correct initial sequence of movesgives rise to a position which is in turn used for the start of thegame. We claim that this chess variant uniquely both integrates andpreserves the legacy of chess (i.e. is forward compatible as well asbackward compatible with the classical game, as defined in 2.4(ii)above).

Shortcomings of Current Solutions Which the New Invention Addresses

These have been considered in 2.2. The current chess variant which mostclosely resembles classical chess is Fischer-Random chess (a.k.achess960), to the exclusion of the invention herein presented. Referringto the three objectives specified in 2.4 above Fischer-Random chessfulfils (i) and regarding (ii), is “backward compatible”, while it isnot “forward compatible”: many, in fact the vast majority(statistically, more than 998 in 1000) of Fischer-Random chess games arenot possible games of classical chess. Additionally, it does not fulfil(iii) either, as it does not reflect opening preferences of contemporaryclassical play (in fact, it does away with chess opening theory).

Note that other variants that introduce new board, new pieces or newrules after the start of the game occurs do not even fulfil condition(i) (and of course, nor do they fulfil (ii) completely, nor (iii)).

Utility Improvements of the Current Solution with Respect to Prior Art

The author claims that switching from classical chess to the new game,or complementing its practice with the new game, particularly frommoderate up to the highest skill levels, likely achieves substantialutility improvements.

The major ones, from which others partly stem, is a significant increasein OTB (“over-the-board”) ratios of play as high-depth, player-specificopening preparation becomes of little use. This is extremely valuablefor the game as a sport (i.e. based on live actual performance of theplayers) and for the interest and delight of the game spectators andresults in more creative play also in the opening.

The players themselves at all levels from strong amateurs upwards, andparticularly at the top competitive level, experience substantialutility improvement in:

-   -   Not having to exert themselves for an inordinate amount of        preparation time in rote opening memorisation, which is        generally seen as most unpleasant (while in the new game        emphasis shifts to understanding of the whole possibilities of        the opening and to pattern recognition, which is the hallmark        human skill used throughout the game)    -   Longer value of the study of the opening made in the past, or        less time needed for it after the opening repertoire in the new        game is built    -   A larger value of making the personal “human capital” investment        of becoming a chess professional or devoted amateur, with        plausibly a longer-duration career, as rote memorisation ability        decreases markedly at senior ages and much less short-term        memory refreshing is needed.

All this happens as the new game preserves the legacy and essence ofchess, which has been seen empirically very important to the chesscommunity and the major obstacle to the growth of chess960. Ourinvestigations also indicate that the possible initial positions are notexcessively forcing or conditioning to a player's style: as strongrandomness is reached for departures from the initial position of a verylow number of moves.

Another important feature of the new game is that contemporaneousclassical chess collective opening preferences and their futureevolution are naturally integrated into the modified new game, as thedistribution of opening sequences mimicks that of contemporary masterplay.

The final, all-encompassing utility improvement is achieved by networkeffects as a new, improved game is made available for an already massivefollowing of chess players.

See paragraph 5 for other benefits, including those affecting casualamateurs and learning players.

All this utility improvements may be the base for generating value,economic and otherwise, through the promotion of new chess events andmethods of implementation described below.

DETAILED DESCRIPTION OF THE INVENTION Conceptual Procedure and Method ofPlay

The invention herein consists of series of steps, together with itsimplementation by software within several types of apparatus and/or itstransmission by electronic or digital means. The procedure includes arandomization step that will result in the selection of a legalclassical chess position from where the game would be started. The newgame would be exactly equal to the game of classical chess from thereon(i.e. following all the classical chess rules), thus differing solely inthe initial position from where the game starts, which will be one amongmany possible ones, as different from classical chess, which starts froma unique position of the pieces, crucially known in advance by theplayers.

Definition of “Neoclassical Chess”

In order to better describe the procedure we define the collection ofdifferent “Neoclassical chess” games, considering all “depths” (numberof full moves), where D is an integer number D=0, 1, 2, 3 . . . For thepurposes of the current patent application, depth D may go from 0 to 10in increments of 1.

Example of meaning: Depth 2 refers to a position in a game two fullmoves after the initial classical chess position, i.e. after the secondmove of Black (note that a full move comprises a move by White and themove by Black which immediately follows after it). In this positionWhite plays next.

Neoclassical chess at depth D (where D is an integer) as the followingway of playing: A game of chess that proceeds in the following way. Justbefore play, a classical chess game is selected at random from areference database of all relevant, correct² contemporary human mastergames, and the position in it after D full moves is designated asinitial position of the Neoclassical chess game. The players start thegame from such position thus obtained. The position in the selectedclassical game is obtained after D moves by White and D by Black, sothat the White player chooses the next move in the Neoclassical chessgame. ² Correct at least up to including full move D.

Note that Neoclassical chess at depth D=0 is precisely classical chess,which we retain for internal consistence of the denomination but whichis not a new game.

We can similarly define slightly different games when D is an integerplus 0.5. Note that this is equivalent to depth being an odd number of“half-moves”, (a “half-move”, as different from a “full move”, is a movefrom only one of the players, either White or Black). We denominate thisvariant “Neoclassical chess with Black pieces” or “Neoclassical Blackchess”.

Where appropriate, “Neoclassical chess” will refer in all what followsindistinctly to “neoclassical chess” or “neoclassical black chess” inthe context of two forms of the same, new game or of the same invention.

We define the collection of different “Neoclassical black chess” games,considering all “depths” (number of full moves) D=0.5, 1.5, 2.5, 3.5, .. . . For the purposes of the current patent application, depth D may gofrom 0.5 to 9.5 in increments of 1.

Example of meaning: Depth 2.5 refers to a position in a gametwo-and-a-half full moves after the initial classical chess position,i.e. after the third move of White (hence it would be the positionreached at Depth 2 plus an additional 0.5 move, which is a half-move byWhite, so its third one). In this position Black plays next.

Neoclassical Black chess at depth D (where D is an integer plus 0.5) asthe following way of playing: Equally as “Neoclassical chess at depth D”above, except that in the “Black” variant, D is not an integer butequals N+0.5 (with N being an integer), so that the position in theselected classical game is obtained after N+1 moves by White and N byBlack, hence the Black player chooses (moves) first in the NeoclassicalBlack chess game.

This will result in a variant of the new game in which positions areobtained such that the last move is a move by White. It is moredifferent from chess than the variant resulting from the whole integerdepths described above. However this additional variation of the newgame has independent interest as White would retain the advantage ofhaving moved first, but Black as partial compensation has the slightadvantage of making the first choice, within the neoclassical game,after the initial position is obtained.

For an illustration of the new proposed game in these two forms, seeFIG. 1 at the end of the application.

Further Explanations on the Terms of the Definition

How is depth D chosen: depth is chosen according to the type of new gamethat is to be played. It can be chosen optimally to be the minimumpossible that obtains a sufficiently large number of positions, in thesense described at the end of 2.4 above, so that preparation by rotememorisation becomes impossible, either in the normal or “black”variants described above. See Appendix I in the current patentapplication for an illustration on how to explore what are thetheoretical optimal depths. Notwithstanding this, even if the depth(s)that best work in practice are to be confirmed by sufficientexperimentation in practical events, the theoretical investigationundertaken for the current invention strongly suggests the best options.Our preliminary analysis, to be confirmed by practical experimentation,suggests that best uses appear to be:

-   -   a. Depths 0.5, 1, 1.5, 2.0 for school chess applications and        amateur training and    -   b. For “neoclassical chess” as is to be customarily played:        depth 3 for a single standard of play at all levels, including        top-level chess.    -   c. For “neoclassical black chess” as is to be customarily        played:        -   i. Depth 2.5 for amateur and non-professional master            competition        -   ii. Depth 3.5 for a single standard of play at all levels,            including top-level chess.    -   d. Depths 4, and above through 10 in 0.5 increments, (including        fractional depths as 4.5, 5.5 etc.) possibly mainly used for        exhibition and opening and training, while depths above 10        mainly for training purposes.

In order to clarify the procedure, we further explain several terms usedin the definition of “neoclassical chess”.

How a game is selected at random: as many games of the referencedatabase will repeat positions at a certain depth, those positions arenot equal-weighted, but appear in the same proportions as those in thecollection, reflecting the distribution of collective openingpreferences of “masters”, which was the condition specified in 2.4(iii). Note that as we draw from the “empirical distribution” of games(the database), for a sufficiently large number of games we obtain thesame (a priori) probability distribution of openings within the new,neoclassical chess game.

What are contemporary games: A sliding “time window” is used. The last Nyears up to the current moment are considered as defining contemporaryplay, where N could be any reasonable number; for example, 5, 10 or 20years. Every year or every few years, the reference database of games isupdated, taking again the previous N years. This also provides for theevolution of chess opening preferences as requested in 2.4 (iii).Example: In January 2016 we would construct the database with allrelevant games from the previous 10 years, 2006 to 2015, both included.In January 2018 the database would be updated and would compriserelevant games from 2008 to 2017. In an alternative process, games fromall recorded history could be used.

What are correct games up to a certain move: We would consider themcorrect if they appear frequently enough in top-level games (where bothplayers are above a certain official rating number, higher than for justqualifying for the database) or the computer evaluation (using aspecified highly-rated compute “engine” or software program) after eachmove changes negligibly, so that the attained position does not deviatesignificantly from that of the initial classical position, or acombination of both criteria

What is relevant human master play: master in a broad sense, i.e.players of sufficiently high skill level, and taking (relevant) ratedplay competitions. The proposal is to take only “rated”³ games whereboth players are above a certain rating (as a possibility 2400 or 2500which correspond to conventional “International Master (IM)” or“Grandmaster (GM)” ratings), while other ratings could be considered.Also reasonable criteria are whether to use only standard (“slow”) rateof play (i.e. time limits used for the chess clock), i.e. eliminatingblitz, rapid and blindfold games which can bias the distribution due tothe specificity of these forms of play, or include at least rapid play.This could be further sophisticated using different variants, apercentile of top-rated players and the rating limit could evolveslightly over the years; this complication adds nothing significantbecause of the slow evolution of preferences. Also, relevant play couldexclude short draws (games that end in a draw after at most a certainnumber of moves) where not much competition may be intended by theplayers, so that they do not bias the database. ³ This “rating” can beobtained from any public sources (international or national federations)or can be assigned by the inventor with a systematic criteriaconsidering several of these.

Specific New Procedure

This section describes the above procedure in more detail regarding theorder of the steps, where we assume the maximum depth of interest Dmaxis given (see above for the meaning of depth in “neoclassical chess” and“neoclassical black chess”).

Construction of the “Reference Database”

-   -   1. A public or commercial database of all relevant games (for        example “rated” human games, and/or from official or so deemed        “serious” chess competitions) is collated and used, in a        standardised public format⁴. ⁴ The PGN format is one such public        format for annotating chess games.    -   2. An initial filtering process is done on the database. This        consists of the following collection of steps, where steps “a”        through “c” can be realised in any different order.        -   a. Eliminating non-contemporary games, where contemporary            games encompass a previous time period before a relevant            reference date.        -   b. Eliminating all games where one of the players is at time            of play below a certain level of rating representing a            sufficiently high skill level. The minimum rating defining            the skill level can be constant over time or can be slightly            adjusted to account for rating “inflation”, taking different            levels in different time frames. Alternatively, accredited            titles can be used as a criteria for qualifying players over            the minimum.        -   c. Eliminating non-relevant games: for instance, use            standard (“slow”) rate of play, eliminating blitz and            blindfold games which can bias the distribution due to the            specificity of these forms of play; in this example            rapid-play may or may not be eliminated. Computer games are            also eliminated.        -   d. Early draws can also be considered for elimination.        -   e. Thus an initially filtered game database is obtained.    -   3. Optional rare opening sequence determination step. Listing        and classifying all distinct positions arising from “opening        sequences” with their corresponding absolute and relative        frequencies (different move orders can give rise to the same        position). Establishing which are “rare occurrences” of such        positions, (i.e. where they appear in less than a pre-specified,        small percentage of cases as e.g. 0.01% or 0.001% and/or in less        of an absolute number of games)⁵. ⁵ This is performed for Dmax,        so that the process does not depend on which is the depth as        long as it is below the maximum.    -   4. Optional filtering by truncation step. A second filtering        process is done on the database (“truncation process”), where        all games which result in an opening sequence which is deemed a        “rare occurrence” are eliminated.    -   5. For each game in the database, each position obtained at the        maximum depth of interest Dmax and the sequence of moves leading        to it is examined, and is approved if:        -   a. The position appears in a sufficiently large fraction of            relevant games where both players have sufficiently high            rating (top-level human chess approval criteria), or        -   b. alternatively, a highly rated software chess engine (e.g.            over 3000+ equivalent human rating, more than any human            player in history), or several such engines via an average,            is used to assess if the resulting position has an            evaluation which differs from the evaluation of the initial            classical chess position less than a certain threshold            (which may or may not be calibrated by the above criteria in            9a).        -   c. In the unlikely case that it is not approved, the game is            discarded, along with all others that lead to the same            position at the maximum depth of interest.    -   6. Thus the final, single “reference database” is obtained,        which is not dependent on the choice of depth. Although the        resulting reference database of games seem to depend on several        design choices, the author claims that these are not too        important for the resulting distribution of openings in the        database, which is highly robust, i.e. differs little, within        broad reasonable ranges of the parameters used above. Hence the        result is non-arbitrary except perhaps by a very small margin of        approximation. Note that the construction of the database is        performed once every year or every few years.

Obtaining the Initial Position in Neoclassical Chess

-   -   The depth D is given.    -   1. A game is chosen at random from the reference database thus        obtained, with all such games having equal probability of being        chosen (uniform probability distribution), using a high-quality        random generator for the problem at hand. Thus any such game        will have a 1/N probability of being chosen, N being the number        of games in the reference database.    -   2. The first D full moves of the game are selected, determining        the “opening sequence”. If D is an integer, the sequence will        end with a move by Black. If D is non-integer, the sequence will        end with a move by White. Note that opening sequences have        different probabilities of being selected, as some may be more        frequent than others at such depth within the database.    -   3. When such D full moves are played as in normal classical        chess from its fixed initial position, a legal classical chess        position will result.    -   4. The position thus accepted is the outcome of the procedure        and will be used for the players of the new game (“Neoclassical        chess”) to start play. In the case that depth D is an integer,        the White player will start play as in the classical game;        otherwise the Black player will. From then on, play will be        conducted as in classical chess.

For other variations of the procedure, please see Appendix II.

Implementation of the Invention

It will use software that will store the “reference database” and ahigh-quality random generator, apt for the large number of games orsequences of moves within the database. Actual implementation of theinvention will proceed along the following lines, including withoutlimitation as a representative sample.

-   -   1. A spreadsheet or software program is implemented in a        computer, personal or otherwise, including the reference        database (which can be simplified to include only opening        sequences or positions) as described above. A random choice is        made on these (uniform in the former, non-uniform in the latter        and according to opening sequence frequencies) and the selected        opening sequence and initial position for the new game is        obtained for the players to start play from. The sequence may        appear in standard chess notation, or the position may appear in        a chess diagram or other equivalent means. This could or could        not be used in conjunction with usual dedicated tournament chess        software for organizing tournaments (be it closed, e.g.        Round-Robin or open tournaments of the new chess form). The        purpose of this implementation is the use for collections of        players: chess clubs, tournament organisers and arbiters.    -   2. Application for websites that manage game playing by large        collections of players online, possibly including computer        programs as players. Similar software programs implementing the        procedure and putting in contact any computer connected to the        internet, in order to play online the new game (neoclassical        chess or neoclassical black chess, each at any depth). The        purpose of this implementation is that commercial and        non-commercial chess-playing websites enable on their sites the        new game.    -   3. An application for smartphones, portable or wearable        computers or physical devices (for instance game consoles, new        or existing). Alternatively, additions or modifications to        already existing physical devices. Such procedures may install        the “reduced form” implementation described in the Appendix II        whenever small memory resources in the computer or device make        it advisable, to avoid a full database of games. The purpose of        this personal implementation is that an individual or small        group of individuals be able to obtain in a fast manner its        random initial position for play.    -   4. A chess program (software) for installation in any computer o        device that would include as an additional feature the        possibility for the buyer of playing the new game with its chess        engine.    -   5. Other additional features to the core capabilities (e.g.        select highest-rated games of the database which feature the        three possible results of win by White, win by Black, and draw).    -   For an illustration of the implementation, see FIG. 2 at the end        of the application.

Other Uses and Benefits of the Invention

The invention could potentially be used similarly in other board gamesof skill where in order to decrease the importance of memorisation ofthe initial position, this is obtained from a random choice from adatabase of actual human games up to a certain move. Some otheradditional or incidental social benefits of the invention are arguableas they include plausible but yet-to-be-proved empirical claims, inwhich the author strongly believes:

-   -   The adoption of the new version of the game of chess invented        plausibly enhances the personal well-being of the aggregate of        professional and elite players once it becomes the standard, as        a result of less exerting and more pleasurable preparation. We        also predict that a transition “investing” period in opening        preparation, whether initially more time-consuming or not, will        lead to shorter total lifetime preparation time (even including        time discounting) at the depths associated with competitive        professional play, and probably at other levels too.    -   The smaller relevance of memorisation for the general, amateur        chess population, results in seniors' relative ability not being        artificially downgraded by the boost that computer-aided        preparation has given to an arguably already-too-large        importance of rote memorisation. In the current state of        affairs, this artificial degradation of the chess performance of        very experienced players (inevitably seniors at some point)        results in discouragement, plausibly reducing their interest in        chess. This is socially negative not only from the interest as a        competitive pastime, it becomes more socially relevant in the        context of recent investigations of chess practice as a tool in        the prevention of Alzheimer.    -   The benefits described within 3.3 may likely result in increased        levels of interest from the chess and wider community. Also, if        the new game becomes popular, although it may partly displace        (“cannibalize”) some interest from classical chess, the        aggregate result (sum total of interest in the classical and        neoclassical game) is also highly likely to increase with the        total number of chess events. It does not seem far-fetched to        speculate that the total economic value of the chess as an        economic activity (and hence salaries and profits over and above        wide amateur satisfaction) can also increase in a more        competitive and less predictable game.    -   Neoclassical chess might well boost the well-established        benefits of chess in schools once an initial chess learning        phase is completed and the opening becomes a subject of study,        as it strongly emphasizes the skill of pattern-recognition (with        its unambiguosly positive impact on intellectual youth        development) over rote memorisation. The benefit is compounded        by the fact that the usefulness of the latter is being        increasingly challenged in the digital era.

Non-Obviousness

We claim that although once known to the public, the current inventionmay in the future be deemed by some to be not excessively complex inretrospect, it is in fact highly non-obvious in its purpose, i.e. as asolution to the current predicament of the game of classical chess.

The concerns that the current invention addresses are very well-knownand publicized and are found in declarations not only of chessobservers, but in those of many of the top current and recent chessplayers, and have been well-known for at least two decades. For theinvention to be a success, it has to find acceptance from a substantialpart of the current chess-playing community; otherwise its value(economic and other) will be small, as value can only be derived from aquantitatively substantial number of chess players wishing to engage inthe new form of the game and to use the new invention. If such successwere in fact obtained by the new invention in the near future, it woulddemonstrate that it is highly valuable. It would be hard to believe thata highly valuable invention would be simultaneously “obvious” and simpleenough to be at reach by many of the massive number of followers of thegame.

We argue that the core of the current invention is not only theprocedure itself but the fact that it serves the purpose of solving themultifaceted, highly constrained problem herein described, thusinvolving a strong counterfactual (leap of imagination) as to the futurecollective reaction to the invention of a given large group ofindividuals (the current chess community) and their evolving reaction asthey test the invention. Thus the invention will be subject itself tothe verdict of an already existing, large group of users, and the veryfact of eventual success would confirm its non-obviousness.

REFERENCES

R. DESJARLAIS, “Counterplay: an anthropologist at the chessboard”.University of California Press. (2011)

R. EALES, “Chess: the History of a Game”. Hardinge Simpole Limited,revised edition. (2002)

S. GIDDINS, “How to build your chess opening repertoire”. GambitPublications (2003).

[Kasparov] G. KASPAROV, “Garry Kasparov on Modern Chess. Part I:Revolution in the 70s “(Chapter 24). Everyman Chess (2007).

The rules of chess960 (Fischer-Random chess) are recognised in the FIDELaws of Chess of the international chess federation (page 22).

https://www.fide.com/FIDE/handbook/LawsOfChess.pdf.

Statistical Analysis of Optimal Depth

For each depth, we obtain the probability density function of resultingpositions, taking into account transpositions (different move ordersarriving to the same position), both in the cases of integer depth(neoclassical chess) and non-integer (neoclassical black chess).

For each depth, we order all positions in decreasing frequency. Withthis order, we construct the cumulative distribution function F,statistical term that allows us to state that, for example, afterBlack's second move the 7 most frequent positions cover 50% or more ofthe games in the reference database. In our formal framework, the“restrictions” of the optimization are those that such function F mustverify. From the results in the database, we construct the table seen asFIG. 2 (using a concrete, representative database for illustration):

The table shows for different depths the probability of the mostfrequent initial position, and how many positions (taking them in orderof decreasing frequency, hence first those more important) a player mustprepare to be assured, with a certain probability, that the initialposition obtained is among those he/she has prepared. For example, atdepth 2 a player must study 7 positions to be have a chance of at least50% that his/her preparation has been useful, and 13 for a 66.6%probability. In statistical terms, the restriction on the uncertainty isexpressed as: F(7)≧0.50 where 7 is the smaller integer that verifies theequation. Also, the most frequent position at depth 2 appears with a11.9% probability, and is that obtained after the sequence of moves inalgebraic chess notation 1. d4 Nf6 2. c4 e6 (where N stands for“knight”). This number 11.9% includes less frequent move-orders leadingby transposition to the same position. An analysis of the resultsindicates that the jump from depth 2 to 3 is significant at all relevantprobability levels of validity of preparation, in particular the veryrelevant 66.6% and 75%, reaching for the first time at depth 3sufficiently high levels (more than 50 positions), and stronglyindicates that 3 is the minimal depth that achieves sufficientuncertainty for all levels of play, including top-level chess. Similaranalyses are carried out in the case of Neoclassical black chess, andare confirmed by the examination of other databases obtained withdifferent parameters.

Variations of the Procedure Modifications of the Procedure:“Variable-Depth” Neoclassical Chess

It may be possible to use different depths, while they result in acomplex game specification, where the depth of the initial position ofthe new game could vary. This is another possible variant, that cannotbe described as a process independent of the actual statisticaldistribution of games, whereas the main form of the new game that wehave described can be determined by the simple choice of the first Dmoves of a random relevant master game, i.e. independent of the actualdistribution of games. However, it is yet a further simple modificationof the original invention.

A modification may be to select initially at random the depth to beused, instead of using a different, fixed depth for different purposes.For example, a random draw would be done from an initial distributionthat assigns a 10% probability to using depth 1, 15% to depth 2 and 75%to depth 3. Then once the depth is obtained, the rest of the steps from1 would follow similarly. This would combine to a “variable depth”version where maximum depth of any initial position is 3.

Another interesting modification of the procedure, at the expense ofconceptual and practical complexity is the following “variable depth”version: construct a database of positions for a certain depth, let ussay 3. Then, keep all the positions unchanged up to a significantcumulative probability (of the most frequent ones) above a significanthigh threshold (75% or 90%). For the remaining marginal low-probabilitypositions, reduce all sequences of moves that can be grouped at a lowerdepth6 (also an integer as 3 is one, so White plays next). There is aninterest in simplifying and grouping in a natural way this infrequentopenings to lower depths, as they do not affect the restrictions on theuncertainty at the key probability levels, which are below thethreshold.

Other “variable-depth” variations are similarly possible. For example,most of the opening sequences could be of depth 3 except one where thesequence has been replaced with 2 sub-sequences of depth 4 with 2respective frequencies adding up to the frequency of the sequence theyreplace. This possible modification may make possible a variant withopening possibilities conforming to some conventional openingclassifications, preexisting or otherwise.

Modifications of the Procedure: Different Order of Steps and Use of a“Reduced Form”

The description in 4.2 condenses the steps of the procedure, butdifferent variations of the procedure may be used. Many of the steps canbe performed in a different order. Without being exhaustive, manypermutations are possible: as a matter of statistical sampling, thesteps in 4.2.1: 2a, 2b, 2c, 2d could be performed later, i.e. after step1 in 4.2.2, by discarding a game that does not pass the criteria andchoosing at random another game, i.e. re-enacting step 1. Similarly,step 3 can be established before steps 1 or 2. Some of the steps areoptional as described.

However, the most significant alternative way in which the proceduredescribed could be enacted, leading to very similar results, is bypostulating a distribution of either opening sequences (with theirrelative frequencies) or initial positions, as representative ofreference play at a certain depth D. This we may call a “reduced-form”distribution, in place of the game database or distribution itself.Hence this non-uniform probability distribution or frequencydistribution of opening sequences (or initial positions) could be thenused to obtain directly the opening sequence by means of generating arandom selection in a non-uniform manner, i.e. taking into account itsfrequency (or “weight” of each distinct opening sequence)⁷. Hence thealternative way of the procedure is: ⁶ For example, all marginal 3 ^(rd)move positions originating in the opening 1. b3, e5 may accumulate toit, so that they would be replaced by it and their combinedprobability.⁷ Note that it is not necessary to unify opening sequencesthat lead to the same position after a certain number of moves, althoughit is also possible to do so.

-   -   Given depth D and database obtained as after 2e (optionally        after 5 above), and using the classification of opening        sequences similarly as above, obtain an opening sequence        database at depth D with its corresponding (absolute, relative)        frequencies.    -   Generate a selection from the non-uniform statistical        distribution of opening sequences.    -   Follow from step 4 of 4.2.2 above.

We claim that the first and the alternative procedure, using a “reducedform” of the database, is essentially the same.

An additional alternative or different order of the procedure would bethe following: “truncating” all games included in the database, so thatthey only contain the full moves of the game up to the selected depth,or that they exclude moves over a certain, single, sufficiently highdepth in order to save memory space. Similarly, in the game databaseadditional auxiliary information (chess event in which the game takesplace, result of the game, etc.) which is not relevant for the procedureabove, is eliminated in order to save on unnecessary information. Theseseem to us to be trivial modifications of the procedure.

Another modification would involve using the reduced form above toimplement the “varuiable-depth” procedure described in 4.2.3. Also,using computer play or a mixed human/computer game collection arepossible, although they do not fulfil all the dimensions of the problemherein described.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a scheme of the implementation showing all elements:

A central processing unit for storing a database of reference (1)

A database of reference created from all recorded chess games in historydivided by categories (2)

A selection and filtering process based on a specific algorithm thatselects one single game in order to stablish the initial position of thenew game (3)

A chess software for installation in any device (4)

Electronic devices to play the new game online (5)

Unlimited number of users to play the game live (6)

FIG. 2 shows a chart showing the statistical analysis of the optimaldepth.

1. Implementation of a new variant of chess characterized because it hasthe following elements: A central processing unit for storing a databaseof reference (1) A database of reference created from all recorded chessgames in history divided by categories (2) A selection and filteringprocess based on a specific algorithm that selects one single game inorder to stablish the initial position of the new game (3) A chesssoftware for installation in any device (4) Electronic devices to playthe new game online (5) Unlimited number of users to play the game live(6)
 2. The implementation of claim 1 wherein the selection and filteringprocess consists of the following steps: eliminating non-contemporarygames, where contemporary games encompass a previous time period beforea relevant reference date eliminating all games where one of the playersis at time of play below a certain level of rating representing asufficiently high skill level, taking different levels in different timeframes. eliminating non-relevant games like slow rate played games,early draws games, blitz and blindfold games and computer games.
 3. Theimplementation described in claim 1 characterized because the startingposition of the game is determined at random just before the start ofplay, being unknown by the players until the beginning of play andwherein the procedure for obtaining that initial position consists ofsetting a certain specified number of full moves, said number beingcalled depth, from the starting position of classical chess and beingthe depths numbers all up to 10 and either integers, except 0, or theresult of adding an integer plus 0.5; selecting at random one game froma single reference database made of high-skill human classical chessplay and regularly updated and initiating the game from the initialposition the player with the white pieces if the depth number is aninteger, otherwise the black pieces would initiate the game.
 4. theimplementation described in claim 1 wherein a statistical analysis toolis introduced within a mathematical framework of constrainedoptimization, in order to determine the optimal depths for competitivepractice, which results are to be confirmed by experimentation.
 5. theimplementation described in claim 1 wherein alternatively for each depththe reference database of games can be converted into a database ofeither positions or initial sequences of play which appear withdifferent frequencies; or variable depth and minor variations in thedefinition of the reference database.
 6. An algorithm for the process ofrandomly determining the initial position of the implementationdescribed in claim 1, which verifies that the probability distributionof the initial positions of the game is representative of that ofcontemporary correct high-skill classical chess play and can be updatedin order to accommodate its future changes, thus being able to track thecollective opening preferences of human master chess.